Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

For professional learning to "stick," teachers need to connect what they learn to their practice--and particularly to their work with their current students. The authors describe a PD program they've developed for math teachers with emergent multilingual students (English language learners) in their classes. Teachers choose "focus…

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Learning experiences regarding the line of best fit are typically students' first encounters with the fundamental topic of statistical association. Students bring with them into these learning experiences prior knowledge and experiences about mathematical lines and their properties, namely slope. This study investigated the role students'…

"Ensuring Mathematical Success for All" (NCTM 2010) outlines eight teaching practices for effective teaching and learning of mathematics. One of the teaching practices, building procedural fluency from conceptual understanding, states the following: Effective teaching of mathematics builds fluency with procedures on a foundation of…

Why do certain objects or images such as a piece of furniture, an item of clothing, or even a flower appear visually attractive? The most obvious factors must involve aspects such as size, colour, movement and discrepancy such as in looking at a Salvador Dali painting. Yet there is another subtle factor associated with shape that also can demand,…

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture…

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

This research was conducted to investigate 7th grade students' problem solving success rates on proportional reasoning problems and whether these success rates change with different problem types. 331 randomly selected students of grade seven participated in this study. A problem test which contains three different types of missing value (direct…

As outlined in the paper "The 20 Matchstick Triangle Challenge: An Activity to Foster Reasoning and Problem Solving" by Pat Graham and Helen Chick [EJ1093090], an incredibly useful set of information about the mathematical ability of your students will be revealed. You can look at the way your students try to solve the 20 matchsticks…

Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is…

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality.…

Mathematical conjectures and theorems are most often of the form P(x) ? Q(x), meaning ?x,P(x) ? Q(x). The hidden quantifier ?x is crucial in understanding the implication as a statement with a truth value. Here P(x) and Q(x) alone are only predicates, without truth values, since they contain unquantified variables. But standard textbook…

This paper describes the development of a concept inventory, a test designed to investigate undergraduate students' understanding of the concept of function. A central purpose was to address "conceptual" understanding. We outline a set of elements of the understanding of function, based on key properties of the function concept, which…

This paper reports and describes some of the observations and conclusions drawn from a study developed to find information on undergraduate students' spontaneous actions and reactions to mathematical definitions that are new to them. There were 23 participants from a transition-to-proof course. They were interviewed individually on a particular…